General summaries on the loadunload and forcerelease methods indicate that the two methods are efficient for different-charactered quasi-static failures; therefore, it is important to choose the right one for different applications. Then we take, as an example, the case where the release of the ruptured element's internal force is infinitely slower than the relaxation of the lattice system and analyze why the forcerelease method works better than the loadunload method in this particular case. Different trial deformation fields are used by them to track the next equilibrium state. Forcerelease method ensures that the deformation throughout the whole failure process coincides exactly with the controlled-displacement boundary conditions and we utilize the 'left modulus' concept to prove that this method satisfies the energetic evolution in the forcedisplacement diagram; both of which are not satisfied by the loadunload method. To illustrate that the forcerelease method is not just another form of the loadunload method, a tensile test on a specifically designed system is analyzed to further compare the above two methods, showing that their predicted sequences of elemental failures can be different. In closing, we simulate the uniaxial tensile test on a beam lattice system by the loadunload and forcerelease methods and exploit the details of the resulting fracture processes.